MinT - Best Known (86−60, 86, s)-Nets in Base 27

Best Known (86−60, 86, s)-Nets in Base 27

(86−60, 86, 114)-Net over F₂₇ — Constructive and digital

Digital (26, 86, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 86, 114)-net over F₂₇, using
- net from sequence [i] based on digital (23, 113)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 23 and N(F) ≥ 114, using
    - an explicitly constructive algebraic function field [i]

(86−60, 86, 150)-Net in Base 27 — Constructive

(26, 86, 150)-net in base 27, using

2 times m-reduction [i] based on (26, 88, 150)-net in base 27, using
- base change [i] based on digital (4, 66, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(86−60, 86, 208)-Net over F₂₇ — Digital

Digital (26, 86, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 86, 208)-net over F₂₇, using
- net from sequence [i] based on digital (24, 207)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 24 and N(F) ≥ 208, using
    - an algebraic function field by Beelen and Pellikaan [i]

(86−60, 86, 5860)-Net in Base 27 — Upper bound on s

There is no (26, 86, 5861)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1257 253903 471995 831345 101468 345934 001650 567341 398881 662332 607955 314319 650508 102558 963476 408531 803253 522392 534396 220364 600849 > 27⁸⁶ [i]